Numerical studies of a multigrid version of the parareal algorithm
| dc.contributor.author | Wambach, Lydia | |
| dc.contributor.author | Turek, Stefan | |
| dc.date.accessioned | 2022-03-24T12:54:14Z | |
| dc.date.available | 2022-03-24T12:54:14Z | |
| dc.date.issued | 2022-03 | |
| dc.description.abstract | In this work, a parallel-in-time method is combined with a multigrid algorithm and further on with a spatial coarsening strategy. The most famous parallel-in-time method is the parareal algorithm. Depending on two different operators, it enables the parallelism of time-dependent problems. The operator with huge effort is carried out in parallel. But despite parallelization this can lead to long run times for long-term problems. Since the parareal algorithm has a two-level structure and the time-parallel multigrid methods are also widespread in the area of parallel time integration, we combine these approaches. We use the parareal algorithm as a smoothing operator in the basic framework of a geometrical multigrid method, where we apply a coarsening strategy in time. So we get a multigrid in time method which is strongly parallelizable. For partial differential equations we add an extra spatial coarsening strategy to our multigrid parareal version. All in all we get a method, which has a high parallel efficiency and converges fast due to the multigrid framework, which is shown in the numerical studies of this work. So we will get a highly accurate solution and can greatly reduce the parallel complexity, which is especially important for long-term problems with a limited number of processors. | en |
| dc.identifier.issn | 2190-1767 | |
| dc.identifier.uri | http://hdl.handle.net/2003/40827 | |
| dc.identifier.uri | http://dx.doi.org/10.17877/DE290R-22684 | |
| dc.language.iso | en | |
| dc.relation.ispartofseries | Ergebnisberichte des Instituts für Angewandte Mathematik;650 | |
| dc.subject.ddc | 610 | |
| dc.title | Numerical studies of a multigrid version of the parareal algorithm | en |
| dc.type | Text | |
| dc.type.publicationtype | preprint | |
| dcterms.accessRights | open access | |
| eldorado.secondarypublication | false |